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Introduction

In this article

• How to interpret stats correctly
  
• Why stats need to be seen in context
  
• The dangers of sample size
  

In the first part you learned about the pyramid system and now know which stats are related to which. The importance of sample size to stats and the principle behind interpreting a stat were also explained.

In this second part you will gain more in-depth knowledge about stats and will learn how to interpret stats and how to deal with sample size. You will also be given an introduction to the concept of an interpretation chain.

At the end of the article you will understand why certain stats with the same value can lead to different conclusions about Villain. Depending on the context, you can interpret the value one way or another. Other important aspects that influence your decision such as board texture, hand history and reads will not be examined specifically in the examples.

You need to familiarize yourself with the thinking process, i.e. understand the formulas, rather than learn certain outcomes by heart.

To interpret a stat in a specific situation, you need to form a complex chain of interpretations. This means you make a series of interpretations on every street, where each of these series has two levels. The first level is examining the stat in relation to other relevant stats.

On the second level you interpret the results on the basis of the actual playing situation. This involves taking all the previous series of interpretations into account and including future streets. The second level of a series is thus the actual interpretation of the conclusions you've drawn about a stat, including the contexts, while not losing sight of all the specific influences that vary depending on the situation, such as board texture, hand history, table dynamics, reads, metagame, etc.

• First level: forming a context chain

You examine a number of isolated stats and look at them in relation to relevant stats for the same street or other streets.

• Second level: interpreting the context chain in an actual playing situation

Added up, this gives you the node of a chain of interpretations for a street.

Of course you base your considerations on the flop on your pre-flop considerations. On the turn you base your considerations on your pre-flop and flop considerations, etc. This in turn forms a complex chain: the interpetation chain.

The following illustrates the structure of an interpretation chain. You can see that every node is connected to all the others. This indicates that you should not only take conclusions from previous streets into account, but also include the stats of future streets in your considerations.

Poker is and always will be a game where you never have all the information, despite all the stats you have at your disposal. The player's form on the day, tilt, distraction and other similar factors can make a player suddenly adopt a very different playing style from the one he usually has. Depending on the player type it's therefore a slippery slope to reduce a Villain to nothing but his stats. 

So not only the distribution and succession of cards are subject to variance, but also the playing style of a Villain during every session.

Stats have a unique way of treating this variance in a poker player's playing style as a statistical average...

Experienced players can get accurate reads on their opponents by observing them closely. They can see how willing a Villain is to take risks at any given time, whether he's on tilt, whether there's a table history between him and the other players, whether he's in good or bad form and suchlike observations.

These metagame factors must be taken into account when interpreting, if your playing style or limit allows for this.

So as you can see, stats must be adapted in many different ways when you are in a hand with a Villain. This basic principle is all the more important the stronger your opponents become and the more you deviate from the usual ABC poker.

We will now take a closer look at one structured way of adopting the necessary thinking processes: the interpretation chain.

The interpretation chain and Villain's range

After having looked at stats from a predominantly isolated point of view in Part 1, you will now learn how stats are connected.

Interpretation chains cannot be given a fixed definition, but must be formed individually every time according to Villain, situation and the available sample size. The examples presented here thus serve to clarify the process, so that you are capable of forming an interpretation chain on your own when you next play at the tables.

The interpretation chain will not only help you draw conclusions about the street you are on at any given moment, but also help you form a plan for your hand on future streets.

The rule here is to focus on Villain's played action when you're in position, and to take Villain's possible reaction into account when you're out of position.

Placing stats in context means that you take other relevant stats into account and regard the stats in relation to these other stats.

I VPIP and I PFR are good examples of stats that are very closely related and which give you a very good impression of Villain's pre-flop style and Villain's range on the flop when you have a big enough sample size. The difference between the two also indicates Villain's pre-flop calling range.

It's impossible to draw up a definitive chart. That's why we've provided a number of examples that ought to illustrate the connections.

Pre-flop: I VPIP – I PFR – I calling range

Considerations:

The smaller the gap (for example Villain with 18/16), the…

• …more aggressively Villain plays his hands pre-flop.
• …more often Villain has initiative on the flop.
• …less Villain makes passive calls pre-flop and the smaller his calling range becomes.

The bigger the gap (for example Villain B with 20/10), the…

• …more passively Villain plays pre-flop.
• …less Villain has initiative on the flop.
• …more often Villain makes passive calls pre-flop and the bigger his calling range becomes.

This example shows how these three stats are directly connected, and what kind of general conclusions you can draw about Villain's flop range.

These connections are an important aspect when regarding a stat in context. It gives rise to a long chain of connections, which can all be interpreted differently, i.e. allow for deviating conclusions when the stat value is identical, depending on the interpretations made before. This is the basic principle behind your context chain.

But never forget: poker will always be a game where you never have all the information, despite all the stats.

On the basis of this first level of interpretation of pre-flop stats, this example illustrates the second level of the context chain, i.e. the relevant flop stats.

Flop: II cbet – II fold to cbet – II raise cbet – AF - WTS

Considerations:

• The more aggressively a Villain plays pre-flop, the more often he gets himself into a situation where he can play a  II cbet on the flop.
• The more passively a Villain plays pre-flop, the more often he gets himself into a situation where he's confronted with a II cbet on the flop.
• The more aggressively a Villain plays (AF), the more often he will bet on the flop.
• The more passively a Villain plays (AF), the less often he will bet on the flop.
• The higher Villain's WTS is, the less often he will fold on the flop.
• The lower Villain's WTS is, the more often he will fold on the flop.

These basic principles are probably nothing new to you. But in connection with the interpretation chain you can already draw some very complex conclusions on the flop here. Many players have a playing style that they rarely deviate from. The worse a player is, the more he remains loyal to his playing style. So it is always conspicuous when a player makes a move that seems to contradict his playing style.

You're playing a hand against Villain A and Villain B. In both cases the Villains raise first in from MP and you call with a pocket pair from BU. On the flop in position you are faced with a continuation bet from both of them. Now you need to interpret this continuation bet. To do this, you use a context chain.

Villain A (18/16) and Villain B (20/10) both have a cbet value of 75%. Now consider what this identical value says about Villain's range if you refer back to the above basic principles for the interpretation level on the flop and the interpretation level pre-flop.

• Villain A (18/16, 75% cbet)
• Villain B (20/10, 75% cbet)

Because Villain A plays more aggressively pre-flop and can therefore place a cbet more often, the range that he has in this spot is not that limited. Villain B is more passive preflop, meaning he bets and raises less. He will therefore tend to have a stronger range on the flop than Villain A – compare PFR 10% to PFR 16% here. A cbet made by Villain B is less often a bluff than it is with Villain A, despite their identical values.

This simple example should therefore illustrate how identical isolated stats (here this is the cbet value of 75%)  are interpreted differently and can lead to different conclusions regarding the strength of Villain's range, if you include other stats in your considerations.

Of course you'll not only be looking at the II cbet value, but also other important values from the interpretation level on the flop, so that you can make a plan for the streets that are still to come. So you already think about how you want to continue playing the hand by using the interpretations from the flop.

• Villain A (18/16, 75% cbet, AF 3.0, WTS 35%)
• Villain B (20/10, 75% cbet, AF 1.5, WTS 50%)

Villain B is generally more passive in this example, and so you will see less action from him such as semi-bluffs on the following streets. Because Villain B generally has a stronger range than Villain A after a cbet on the flop, a 2nd barrel on the turn should be considered more relevant than a 2nd barrel on the turn by Villain A.

If you now continue to interpret the cbet value and also include the AF and WTS, it is most probable that Villain B will let out most of his aggression on the flop when he has a cbet flop of 75% but only 1.5 AF.

Your plan for the turn might look like this in this case:  if Villain B shows more action, you fold with a pocket pair for example, or, alternatively, check behind in position to see a free river card or use a float, although this will not always be a very good idea when you're looking at a WTS of 50%. It must be added here that these considerations can be supported by other stats, such as the III turn cbet or the flop AF and turn AF.

As you know already, you need a corresponding sample size for every further stat level. You need to incorporate this important basic principle into your considerations, if you wish to include the III turn cbet for example.

These considerations are based purely on stats on the first level. We will shortly explain how to interpret these thoughts on the second level with an actual playing situation.

The AF and WTS are very useful on the flop, as you saw in the example, although they only represent general values, and are thus not dependent on the flop.

Generally you can say that a higher AF with a low WTS and a low AF with a high WTS are correlated. This is because aggressive players often win their hands with fold equity without going to the showdown, which lowers their WTS.

It's important here to always interpret the AF and WTS in connection with the values from the first interpretation level pre-flop (VPIP, PFR, calling range), as the WTS in particular is relative to the flop range, as you already learned in the first part of the stat series. 

Things to consider when looking at the WTS:

• The higher the WTS, the bigger Villain's range is on the showdown.
• The smaller Villain's flop range is, the stronger his range on the showdown with identical WTS.
• The bigger Villain's flop range, the weaker his range on the showdown with identical WTS.
• The higher the AF, the lower the WTS.
• The lower the AF, the higher the WTS.

Now you've seen exemplary considerations for the first level: context. You've probably already given some thought to how you also need to take important details such as the actual board texture into consideration to form solid judgements about Villain.

On the second level you interpret these results by looking at a real playing situation. Board texture, table dynamics, reads, hand history and all sorts of other factors play an important part in this.

The outcome is an interpretation node. In this example we're looking at one for the flop.

The second level of an interpretation node, i.e. actually interpreting a real playing situation, is very complex. You need to apply all the basic principles that were discussed in the other strategy articles and which will not be discussed any further in this article. 

This example should have clarified how extensive your considerations can be even when interpreting just one stat. You've now seen that stats from other streets can help you when interpreting the street you are on at the time.

You're familiar with sample size. It indicates how many of a Villain's hands you have in your poker database. You also know by now that this stat is very important for your interpretations, as the value of all the other stats directly depends on it. You were already given an introduction to these basic principles in Part 1 with the help of the pyramid system. 

Problems with stats and sample size

Before interpreting any stat, you should first take a look at the sample size, so that you have a sensible basis for your interpretations.

If the sample size is too small for the level you're on, for example on the turn, it helps to take at least those stats that need a much smaller sample size into consideration. These are all the stats from the first level, i.e. the VPIP and PFR in particular.

But it's important here that you do not draw conclusions from stats that need a much larger sample size. If you have just 50 hands, for example, you should definitely not take turn stats such as the 2nd barrel or Villain's 3-bet value pre-flop into account. Many tracking programs will display these even when your sample size is very small in the overlay.

To not fall into the "small sample size trap", you need to get into the habit of automatically taking a look at the sample size first, before you look at any other stat.

If the sample size is not big enough to place your opponent in a rough player type category, you need to treat him as an "unknown player".

Who is this "unknown player" you often hear about? What are the most important assumptions you can make about him?

The unknown player is heavily dependent upon the game variant and the dynamics of the limit. An NL10 unknown is therefore regarded in a very different way from a NL100 unknown. 

We assume that an unknown player has an average level of poker knowledge for the limit being played. An unknown player will also play every action on all the streets in a way that is typical of that limit. So on a passive limit we'd also assume to see more passive playing styles.

So you should look at an unknown player as playing like an average regular at the limit in question. You don't regard him as an exceptional player and can assume he will play a basically logical game that is typical of the limit. 

This approach is interesting when your stat overlay doesn't display certain stats or when your sample size is not enough for stats at higher levels (e.g. on the river). 

Let's assume you're on the flop with a large enough sample size to make interpretations about your opponent on the second level, so about 500 hands, but you want to be able to make a good estimation about the probability of a III 2nd barrel.

The basis for this deduction are Villain's flop range as PFA, i.e. his I PFR value, his II continuation bet flop value and the general stats of Villain's AF and WTS.

Interpreting these stats allows you to draw conclusions about the probability that you'll see a III 2nd barrel on the turn. When playing at a table you must of course also take the metagame and other important factors such as the board texture, position, number of opponents, etc. into account.

So you need to see deduced stats in context too and interpret them accordingly. 

So it's quite possible to work out missing stats from the stats you have available. The interpretation of stats and the interpretation chain provide you with useful thinking patterns for analyzing Villain's style more closely and for seeing every single stat within the entire context. You can gauge the playing style with this and think about how a "missing stat" fits in with Villain's playing style.

But of course the rule again here is: sample size is crucial.

This can often happen. Villains also develop their game more or less successfully, depending on the limit. Because of this, regulars, who you often see at the tables and for whom you therefore have correspondingly high sample sizes, will particularly adapt their playing style and stop giving certain leaks over time. 

Just think about the fact that you are also a regular at a limit yourself, and ask yourself how strong your current play deviates from how you were playing some months ago.

So it makes sense to pay more attention to a current sample size than to a big sample size with many hands that are, however, a number of months old. But if in doubt, too many hands are always better than too few.

The basic rule here is: the less specific a stat is, the more stable its development will be. Good examples here are the I VPIP and I PFR.

Stats that depend on a given situation tend to oscillate more. A check-raise on the turn thus depends more on the individual circumstances when you make the decision.

Can you reduce a Villain to his stats?

You should be able to answer this question easily now. You know that stats are a depiction of statistical averages that need to be interpreted on two levels, and so they are not particularly meaningful in themselves. 

The first level is the interpretation of statistical averages among one another in context.

The second level is the interpretation of considerations from the first level during a specific playing situation in a hand, while taking board texture, hand history, table dynamics, reads and all other influences that vary depending on the situation.

If you regard Villain's moves as one whole, you will come to the conclusion that the sum of all stats are a much better indication of Villain's playing style than his hole cards. 

Every stat is a facet of Villain's playing style to you. If you learn how to interpret these facets accurately, you will be able to draw many conclusions that will help you to make any decisions at the time.

Conclusion

In this article you learned that despite all the possibilities that tracking programs have to offer you, it's still up to you how to handle all the collected information. 

A value must be interpreted correctly for it to help you make a profitable decision in the game. A value seldom stands alone and you should always see it in the relevant context. The interpretation chain illustrates how extensively it can be used when doing so.

If you've understood the contents of this article and you are aware of the dangers and pitfalls, you will soon be able to integrate a powerful weapon into your game when battling for the chips.

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Related articles: Stats (1) - Basics